There are a number of different ways that you can approach this project, some more decorative than others and some that require a bit more skills than others, so I'll give you a number of different ways that you can approach this project. The first two methods that I will mention will require some knowledge of sewing. Being that I have a penchant for it, these were the first to pop into my head, but I know not everyone feels comfortable around the needle and thread, so if it's not for you then I've devised a perfect 3rd solution that you can go ahead and scroll right down to...

Method 01

Velcro Straps. This is an old craft trick that will work out for you, but really only if you have a light-weight rug. You'll want a large strip of velcro to work with for this, much like this Industrial Strength 15 ft. x 2 in. Tape. You'll take one side of the strap and sew it onto the top of the back of your rug. I'd recommend that you use a closer thread and a tight zig-zag if your machine has variable settings. The other half of the strap will be mounted onto the wall and I'd suggest placing a piece of 2" x 2" wood onto the wall first and mounting it onto that. This way your tape won't peel off the paint and drywall when you remove it later on.

Method 02

Cloth Rings. Using a heavy duty fabric material, cut small pieces of fabric out that you can sew on as rings to the back of the carpet. Since this is a bit of close quarters maneuvering, you'll need to do the stitching by hand to attach the rings onto the back of the carpet. Again, I would only use this for light-weight rugs if possible since all your weight is going to be hanging from those rings. You can then attach the rings up using either a dowel rod, screwed into a wall anchor piece of wood, or a curtain rod to make it more decorative.

Method 03

Rug Hanger. The best part about this idea is that no sewing is required and you have nothing that will damage or puncture the material of your rug. This rug hanger will act as a large clamp and hold the rug between the two pieces of wood in the build. However, since it's a bit complex to explain in writing, I did a mock-up build of one for you and gathered a list of materials for you as well. Take a look:

[1 or 2] piece(s) of 2" x 3" x 8" piece of wood. [Note: Whether you're orienting the portrait or landscape style, you'll want to add 2" to the actual size of the rug when making your cut. For example, if I'm hanging the 5' side and the 7' will be hanging down, then I want my wood piece to be 62" (60" + 2")

[1] piece of decorative moulding. [Note: This is optional, but really dresses up the piece. You can opt to use (2) pieces of the 2" x 3" wood for a simpler look, however this build uses a decorative moulding.

Here are the two pieces of wood that I'm working with. The more decorative piece is in an Egg & Dart style that I really thought looked sharp for the project. The bottom is my 2" x 3" piece. For this build I cut them both down to exactly 48". As you can see on the backs of the pieces, you'll want to make sure that any decorative piece you use is
flat on the backside, or else it won't work for the purposes we need it to.

Take your two pieces and clamp them together for the next step. You'll then want to measure out where you are going to drill your holes for the screws we'll be using. Make sure to evenly disperse them and
do not drill through the center of the wood. Notice how the hole that I made is slightly closer to the top of the trim? You'll want to be sure to replicate this and move your marker up from center or else the clamp effect won't work.
Once you have your holes drilled, make sure that the screws you are using fit through and leave enough excess on the other side. Since I'm using a much thicker trim piece, I had to swap out the screws that came with my handles, because they were too short. I ended up using 2" machine screws instead.
Another thing to note about the screws that came with the handles, is that they are all rounded heads. Normally this is fine, but we want a flat backing to our piece, so it just won't cut it. The machine screws that I mentioned above came with a flat head which worked out much, much better.
I also took the time to use my bit to counter-sink my holes, so that the screw will fit in snugger and tighter to the wood. You don't need to go very deep, just a slight bit below the flush level is just fine. Put your screws through the pieces of wood and tighten the knob down. The knobs are there to hide the exposed screw and give a more decorative look.
And here is the completed piece! What you'll do from here is loosen the screws just a bit from the back and insert the edge of your rug in-between the two pieces of wood and have them push right against the screws. Then tighten it down as best as you can and there you go! Place some hanger hooks on the back of the flat 2" x 3" so that you can use it to mount onto the wall (be sure to anchor it properly into the stud!) and then step back and marvel at your creation!
It's something a bit different, but I think it will look really great when it's said and done. You can opt to stain the top trimwork if you'd like, but I enjoyed the natural finish that it came with, so it's up to you!~
Let me know what you think of these ideas or if you'd like to discuss them further!~

I like the simplicity of your rug hanger; however, three other articles I read, by experts in textiles, stated emphatically that you should paint any wood that comes in contact with fabric, to prevent acids from the wood from staining the fabric.

You don't necessarily have to paint the wood. If you wanted the natural wood color to be present, you can simply use some clear stain, shellac, laquer or polyurethane, in the finish of your choice. Jay mentioned staining the wood, the Minwax stain sold by THD has a bit of sealer in it, as that's how the pigment in the stain is held to the wood. The sealer acts as a binder (glue) for the pigment.

Like he mentioned, djdaniel, you don't have to paint it nor do you have to stain it. I just thought that the piece that I picked out had some character to it already and I opted to leave the color as is, but you can optionally stain it if you so desired. A good point you brought up though, so thank you for sharing it with the rest of the community!~ = )

I realize that this is a very old post but am hoping you will reply. I have a heavy wool rug that I want to hang on the wall. Have followed you instruction for the rug hanger and have 2 pieces of wood and handles ready. 2 questions are unclear for me. 1st - hoe far from the center I have to drill the holes. 2nd - what type of hardware I sold be looking for for to mount it on the wall. You are mentioning some hanger hooks on the back. Grateful if you could specify what goes on the wall and what goes on the wood piece. It is my understanding that it needs to be hang pretty flat so not much is seen when you looking on the left/right side of the rug. Many thanks!!!